1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at distance y from the foot of the tower (x > y). The angles of elevation of the top of the tower from P and Q are 15° and 75° respectively.

What is the length of the tower ?

A
$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
B
$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
C
$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
D
$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the value of cosec$\left(−\frac{73 \pi}{3}\right)$ ?
A
$\frac{2}{\sqrt{3}}$
B
$−\frac{2}{\sqrt{3}}$
C
2
D
−2
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the value of $\cos \left(\frac{5 \pi}{17}\right)+\cos \left(\frac{7 \pi}{17}\right)+2 \cos \left(\frac{11 \pi}{17}\right) \cos \left(\frac{\pi}{17}\right)$ ?
A
0
B
1
C
4 cos$\left(\frac{6 \pi}{17}\right)$ cos$\left(\frac{\pi}{17}\right)$
D
4 cos$\left(\frac{11 \pi}{17}\right)$ cos$\left(\frac{\pi}{17}\right)$
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What is the value of tan$\left(\frac{3\pi}{8}\right)$ ?
A
$​\sqrt{2}$ − 1
B
$​\sqrt{2}$ + 1
C
1 − $\sqrt{2}$
D
−($\sqrt{2}$ + 1)
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